Problem SOLVED!!!
Take this folder
http://www.box.net/shared/guv5op29t50easivt35i
Use it to replace this Steam\steamapps\common\il-2 sturmovik cliffs of dover\parts\core\FF
And that is it! Soft centring spring, no shaking when shooting, feedback is there but is very mild, not ultra violent like it always used to be.
I was looking for this kind of solution for MONTHS!
I got the files and the idea to substitute from Suhkoi russian forums.
For some reason this method did not work for me with the previous patches, but now I have restarted CloD several times and the changes did stick and continue to work beautifully. Bf109 is now nicely controllable in dives without having to nearly break my joystick.